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  The 30-year-old London 2012 gold medallist recorded 8.18m in his final jump to win ahead of Uruguay's Emiliano Lasa (7.96m).
  Holly Bradshaw set a new British women's pole vault record of 4.80m.
  There was a minute's silence before the event for the victims of Monday's attack in the city.
  Twenty-two people were killed and another 116 were injured by a suicide bomber as the crowd left a performance by US singer Ariana Grande at the Manchester Arena.
  The Great City Games, which is staged in the city centre, was given the go-ahead by council and police on Tuesday.
  The Great Manchester Run will also go ahead this Sunday and will be covered on BBC One from 12:30-14:30 BST.
  Friday's competition was the first major event in Manchester since the attack and drew thousands to a sunny Deansgate and Albert Square.
  The latter, which three days ago hosted a vigil for those who lost their lives in the attack, was the scene for a stellar display from Rutherford.
  His jump of 8.08m in his second attempt had already ensured victory before his final effort, which saw him extend his lead further.
  "It's been absolutely amazing to get you all out here in support of us," said Rutherford afterwards. "It's been an incredibly difficult week for everybody and I'm so pleased we can come here and give you something to smile about and enjoy.
  "Manchester is one of my favourite cities in the world to go to. I love it for the football and I love it for all you guys getting behind us in sport.
  "It truly is a special place."
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  It was a superb evening for Bradshaw, who beat her own personal best before going on to surpass her own British record in the pole vault.
  Starting at 4.50m, the 25-year-old from Preston cleared at the third attempt to ensure victory over her rivals, with fellow Britons Rachel Gibbons and Sally Peake and Belgium's Chloe Henry all failing to go higher than 4m.
  She then went on to surpass the mark of 4.71m she set in 2012 before also clearing 4.80m at the first attempt.
  "It was a bit nerve-wracking at the start," Bradshaw, who was sixth at London 2012 and fifth four years later in Rio, told BBC Sport.
  "But there were great conditions. Once I got in the zone, to jump 4.72 and then 4.80 I am really chuffed.
  "Training has been going great. I am in the best shape I have ever been in. I just need to stay healthy, keep sharp and build momentum going into the majors."
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  Jonnie Peacock eased to victory in the T44 men's 100m in 10.92 seconds, accelerating to pull well ahead of his three challengers.
  South Africa's Arnu Fourie was second (11.25secs), with Michail Seitis third (11.39) and Italy's Emanuele di Marino fourth (12.18).
  "We had a massive shift on technical aspects last year and had just six months to get them right before the Olympics but we improved a lot," Peacock told BBC Sport. "I still have a lot to improve. My first five metres today were terrible."
  Sophie Kamlish made it a British double in the event with victory in the T44 women's 100m, beating Dutch three-time Paralympic gold medallist Marlou van Rhijn by 0.02secs in a time of 13.24.
  On the specially laid track on Deansgate, Asha Philip pipped Australian Sally Pearson to the win the women's 100m in a time of 11.48secs.
  Pearson made up for that disappointment by winning the final race of the evening - the 100m hurdles - in 12.81secs.
  Another Briton, James Dasaolu, clocked 10.25 to take the men's 100m after 41-year-old Kim Collins, who claimed gold at the 2002 Commonwealth Games in Manchester, pulled up with cramp.
  American Johnny Dutch, who was coaxed out of retirement last year, impressed in the men's 200m hurdles with a time of 22.48secs, comfortably beating a British trio led by Sebastian Rodger (22.89).
  There was a surprise result in the men's 150m as Greece's Lykourgos-Stefanos Tsakonas claimed a personal best of 15.04secs to see off the challenge of Britain's Harry Aikines-Aryeetey, who also ran a PB of 15.22.
  Fellow Briton Richard Kilty was third in 15.43.
target: Britain's Greg Rutherford claimed a resounding long-jump victory at the Great City Games in front of a big crowd in Manchester's Albert Square.